Quantum geometry driven finite-momentum exciton fluctuations in flat-band systems

Abstract

Quantum geometry is instrumental in stabilizing exotic phenomena in systems ranging from topological insulators to superconductors. In dispersionless flat bands, where the kinetic energy is quenched, the quantum metric emerges as the fundamental driver of macroscopic collective phenomena. Here, we theoretically demonstrate that lattice-geometry-induced flat bands, such as those in kagome and Lieb lattices, provide a fertile platform for realizing a quantum-geometry-driven excitonic insulator (EI) phase. By applying an out-of-plane Zeeman field to lift spin degeneracy without spin–orbit coupling, we establish a Ginzburg–Landau framework in which the electron–hole wavefunction-overlap directly maps the flat-band quantum metric onto the macroscopic free energy. This mapping plays a key role in both the EI and the associated superfluid phases, with the coherence length and phase stiffness emerging directly from the quantum metric. Our analysis reveals that under strong interactions, the quantum metric reverses the sign of the kinetic coefficient of the amplitude mode. Rather than destabilizing the uniform condensate, this enhances the amplitude fluctuations at a finite momentum, giving rise to a finite-momentum superfluid density fluctuation (FMSDF) regime. A qualitative signature of the FMSDF regime is shown to be an enhanced finite-momentum susceptibility of the in-plane magnetization amplitude. Our findings establish a rigorous link between the flat-band quantum geometry and dynamic collective excitonic states, and suggest covalent-organic frameworks (COFs) as promising candidates for materials realization.